In a radio communication field, there has been proposed the MIMO technique for suppressing channel fading and improving channel capacity. In a radio communication system using the MIMO technique, transmission and reception of signals are performed between a plurality of transmission antennas and a plurality of reception antennas. Then, a data stream transmitted from each transmission antenna is subjected to precoding thereby to suppress interference between data streams. In a precoding technique using a codebook, a codebook of the same definition is stored in advance in a transmission side and a reception side (for example, a base station and a user terminal in the downlink). During transmission of signals, the reception side selects an optimal codeword from the codebook and feeds back it to the transmission side. After that, the transmission side uses the codeword (for example, single user MIMO, SU-MIMO) or a matrix obtained by processing of the codeword (for example, multi user MIMO, MU-MIMO) to perform preceding of transmission symbols. Conventionally, there are two schemes of recessive feedback and dominant feedback. The recessive feedback is such a scheme that when the reception side considers elements of capacity of its receiver, it selects a codeword to maximize a system capacity or reception signal quality as an optimal codeword and feeds back a preceding matrix indicator (PMI) indicating the optimal codeword to the transmission side. The dominant feedback corresponds to a method of channel vector quantization (CVQ) and generally has no relation with reception power. That is, in the dominant feedback, a codeword that is closest to the channel direction or the channel matrix is selected from the codebook and a channel direction indicator (CDI) indicating the codeword is fed back to the transmission side. In some cases, these schemes are close to each other and replaceable. Existing codebooks (for example, including precoding matrix codebook or channel quantization codebook) include a codebook used in a closed-loop spatial multiplexing mode defined in 3GPP LTE (Long Term Evolution)/LTE-Advanced Release 8 and 10 (hereinafter referred to as “Rel. 8/10”) or constant modulus codebook such as DFT codebook, and non-constant modulus codebook such as Grassmanian codebook.